12.6 Parameterized circuits

The Z gate is fixed in the amount it rotates around the z-axis, while the general R_φ^z gate has the variable parameter φ. When we include such a gate in a circuit, we get a family of circuits that vary with φ. We need such circuits for NISQ algorithms, and we have seen examples of them before.

In section 10.1.3, we developed the circuit for the Quantum Fourier Transform on three qubits and denoted it QFT₃. circuit$parameterized

Figure 12.17: The Quantum Fourier Transform on three qubits

The z-rotations follow a pattern, with angles equal to π divided by powers of 2.

Let’s add a parameter t to the rotation angle, as shown in Figure 12.18. When t = 0, each rotation gate is trivial and is the ID gate. When t = 1, we have QFT₃. We call this circuit with a single parameter U(t).

Figure 12.18: 1-Parameter Quantum Fourier Transform on...